Pseudo-almost automorphic solutions to some second-order differential equations

Toka Diagana; Ahmed Mohamed

doi:10.4067/S0719-06462011000300007

Authors

Toka Diagana Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, D.C. 20059 - USA.
Ahmed Mohamed Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, D.C. 20059 - USA.

DOI:

https://doi.org/10.4067/S0719-06462011000300007

Keywords:

exponential stability, sectorial operator, hyperbolic semigroup, almost automorphic, pseudo-almost automorphic, autonomous second-order differential equation, Sine-Gordon equation, amenability, Banach modules, module amenability, weak module amenability, semigroup algebra, inverse semigroup

Abstract

In this paper we study and obtain the existence of pseudo-almost automorphic solutions to some classes of second-order abstract differential equations on a Hilbert space. To illustrate our abstract results, we discuss the existence of pseudo almost automorphic solutions to the N-dimensional Sine-Gordon boundary value problem.